Which of the images above represents a proof pf the Pythagorean Theorem? Explain your choice, and then explain how the figure proves the PT.
Figure B proves the Pythagorean Theorem.
As you may have noticed, the lengths given for both figures are already perfect squares. All you have to do is add the lengths of the legs to see if they equal the length of the hypotenuse/diagonal.
Figure A: 9 + 36 = 46... not 64
Figure B: 25 + 144 = 169... correct
Figure B proves the Pythagorean Theorem.
Pythagorean Theorem Formula: a^2 + b^2 = c^2
(The numbers are already squared, so just plug them in for a, b, and c, and see if it is a true statement.)
Hope this helps and I hope it made sense.
Which image?
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As an AI, I'm unable to see the images you mentioned. However, I can explain the Pythagorean Theorem and how it can be proven.
The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
To prove the Pythagorean Theorem, there are a few different methods, and one of the most common and accessible methods is through the use of squares.
One way to prove the Pythagorean Theorem is by constructing squares on each side of the triangle. Imagine a right triangle with sides a, b, and c, where c is the hypotenuse.
To do the proof, you would begin by constructing four squares, one on each side of the triangle, with the lengths of their sides equal to the lengths of the triangle's sides.
In the end, you would find that the sum of the areas of the squares built on the two shorter sides (a and b) is equal to the area of the square built on the hypotenuse (c). The equality of the areas proves the Pythagorean Theorem.
Now, going back to the images you mentioned, please describe each image, and I will help you identify which one represents a proof of the Pythagorean Theorem, if available.